Nutational gravitropism is a fascinating plant movement where stems or roots grow in a spiral or oscillating pattern in response to gravity. If you're looking to observe this phenomenon in outdoor plant boxes, certain plants are particularly effective at showcasing it.

1. Morning Glory (Ipomoea purpurea): This climbing vine exhibits pronounced nutational movements as it searches for support. Its twining stems spiral gracefully, making it ideal for observing gravitropism.

2. Sweet Pea (Lathyrus odoratus): Known for its delicate tendrils, sweet pea demonstrates clear nutational growth as it wraps around structures, responding to gravity and light.

3. Hop Plant (Humulus lupulus): A vigorous climber, hops display strong nutational gravitropism, with stems spiraling as they grow upward.

4. Runner Beans (Phaseolus coccineus): These fast-growing plants show distinct nutational movements, making them perfect for outdoor plant box experiments.

5. Passionflower (Passiflora spp.): With its intricate tendrils, this plant exhibits elegant nutational growth patterns as it climbs.

For best results, provide trellises or supports in your outdoor plant boxes to encourage these plants to showcase their natural movements. Observing nutational gravitropism not only adds beauty to your garden but also deepens your understanding of plant behavior.